Microwave studies of the Gaussian symplectic and the chiral ensembles

混沌系统谱的普遍性质，如相邻特征值的间隔分布，与具有相应对称性的随机矩阵系综谱的性质一致。这种普适性是同时得到证明的波希加斯、詹诺尼、施密特猜想的本质。具有时间反转对称性(TRS)且无自旋1/2的系统可用高斯正交系综来描述，自旋为1/2的系统可用辛系综来描述，而具有破缺TRS的系统可用酉系综来描述。对于GSE，我们在本项目中首次实现了随机矩阵理论(RMT)在微波图中的实验实现，这是一个具有特殊对称性的网络，模仿自旋1/2系统。在这个项目的继续中，我们计划研究GSE图的散射性质。除了本申请中描述的我们小组的第一个实验外，这是一个全新的研究领域。对于具有粒子-反粒子对称性的系统，出现了三个新的随机矩阵系综，分别是手性GOE、GUE、GSE。在我们的第一个应用中，我们提出了在介质柱建立的石墨烯的微波当量中实现手性GOE。由于申请中描述的原因，我们决定改用一个更简单的系统，它已经表现出手性对称性，即直线链。正在进行的实验已经证明，我们已经成功地实现了手性GOE。在延伸中，我们计划将研究扩展到手性GUE和手性GSE。这个项目的主要目标，包括它的延伸，是第一次实验实现10个随机矩阵系综中的4个。通过外部驱动二极管和T结的组合，可以产生非平稳图形。利用GSE图中的周期时间依赖关系，我们计划实现自旋共振的微波等效。即使是自旋弛豫的等价物，也可以通过附加应用随机变化的时间依赖性来建立。这将为自旋松弛理论的测试开辟一条新的途径。

The universal properties of the spectra of chaotic systems, e.g. the spacing distribution of neighboring eigenvalues, coincide with those of random matrix ensembles with corresponding symmetries. This universality is the essence of the meanwhile proven conjecture of Bohigas, Giannoni, Schmit. Systems with time-reversal symmetry (TRS) and no spin 1/2 are described by the Gaussian orthogonal ensemble (GOE), those with spin 1/2 by the symplectic (GSE), and those with broken TRS by the unitary (GUE) ensemble.There is an abundant number of experimental realizations for the GOE and a small number for the GUE. For the GSE the first experimental realization after 50 years of random matrix theory (RMT) had been achieved by us in the present project in a microwave graph, a network with peculiar symmetries mimicking a spin 1/2 system.In the continuation of this project we plan to study the scattering properties of GSE graphs. Apart from a first experiment in our group described in this application, this is a completely new field of research. Also RMT, well established for the GOE and the GUE, still has to be developed in mayor parts for the GSE.For systems with particle-antiparticle symmetries three new random matrix ensembles appear, the chiral GOE, GUE, GSE, respectively. In our first application we proposed to realize the chiral GOE in a microwave equivalent of graphene set up by dielectric cylinders. For reasons described in the application we decided to change to a much simpler system, which already exhibits chiral symmetry, the linear chain.The ongoing experiments already demonstrate that we had been successful in the realization of the chiral GOE. In the prolongation we plan to extend the studies to the chiral GUE and the chiral GSE. The main objective of this project including its prolongation is the first experimental realization of four of the ten random matrix ensembles.By means of a combination of an externally driven diode with a T junction non-stationary graphs may be generated. Using periodic time dependencies in a GSE graph we plan to realize a microwave equivalent of spin resonance. Even an equivalent of spin relaxation can be established by applying in addition a stochastically varying time-dependence. This would open a new access to the test of spin relaxation theories.